Dependent T and existence of limit models

Saharon Shelah

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arXiv · math/0609636

Dependent T and existence of limit models

Saharon Shelah

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Abstract

Does the class of linear orders have (one of the variants of) the so called (lambda, kappa)-limit model? It is necessarily unique, and naturally assuming some instances of G.C.H. we get some positive, i.e. existence results. More generally, letting T be a complete first order theory and for simplicity assume G.C.H., for regular lambda > kappa > |T| does T have (variants of) a (lambda,kappa)-limit models, except for stable T? For some, yes, the theory of dense linear order, for some, no. Moreover, for independent T we get negative, i.e. non-existence results. We deal more with linear orders.

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BibTeX RIS

Saharon Shelah. 2006-09-22. Dependent T and existence of limit models. https://arxiv.org/abs/math/0609636

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